Can I use the Arduino Duemilanove to program & test the chip before moving it to my bread board, or will the chip only work when it's in the Arduino environment?

If developed on the Duemilanove then the 168 chip can be moved to the breadboard and needs only a 16mhz resonator or crystal(with caps) and a pull-up resistor for the reset pin.

Or if you get a standalone USB serial converter cable or module you can actually develop the application while the chip is still on the breadboard. It is only requires that your AVR chip has a bootloader already burned into it, several vendors sell them.

Below is the USB serial module I use to develop programs on the breadboard using the Arduino IDE software. I've soldered header pins to it and it plugs into the breadboard. It uses the same USB chip that the Arduino modules use.